Relate Division and Fractions

10 min

Narrative

The purpose of this True or False is for students to demonstrate strategies and understandings they have for interpreting a fraction as division of the numerator by the denominator and vice versa. These strategies help students deepen their understanding of the relationship between division and fractions where the unknown is the numerator, denominator, or the value of the quotient.

Launch

  • Display one statement.
  • “Give me a signal when you know whether the statement is true and can explain how you know.”

  • 1 minute: quiet think time

Teacher Instructions
  • Share and record answers and strategy.
  • Repeat with each statement.

Student Task

Decide if each statement is true or false. Be prepared to explain your reasoning.

  • 5÷2=525 \div 2 = \frac{5}{2}
  • 52=512\frac{5}{2} = 5\frac{1}{2}
  • 62=3\frac{6}{2} = 3

Sample Response

  • True. If I divided 5 into two equal groups, there will be 5 halves in each group.
  • False. 52=5÷2\frac{5}{2}=5\div2.  If I divide 5 into two equal groups, there will be less than 5 in each group. 
  • True. Six halves is equal to 3 wholes.
Activity Synthesis (Teacher Notes)
  • Display:
    • 5125\frac{1}{2}
    • 52\frac{5}{2}
  • “How are these expressions the same? How are they different?” (They both have 5 and 2 in them. They both show halves. 5125\frac{1}{2} means 5 wholes plus one half and 52\frac{5}{2} means 5 groups of one half.)
Standards
Addressing
  • 5.NF.3·Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. <em>For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?</em>
  • 5.NF.B.3·Interpret a fraction as division of the numerator by the denominator <span class="math">\((a/b = a \div b)\)</span>. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. <span>For example, interpret <span class="math">\(3/4\)</span> as the result of dividing <span class="math">\(3\)</span> by <span class="math">\(4\)</span>, noting that <span class="math">\(3/4\)</span> multiplied by <span class="math">\(4\)</span> equals <span class="math">\(3\)</span>, and that when <span class="math">\(3\)</span> wholes are shared equally among <span class="math">\(4\)</span> people each person has a share of size <span class="math">\(3/4\)</span>. If <span class="math">\(9\)</span> people want to share a <span class="math">\(50\)</span>-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?</span>

20 min

15 min